244 Scientific Proceedings, Royal Dublin Society. 
If we integrate this all round the point we have calling 
fate ie 
Qari 
oN =) dt 
when of course 7, is a function of ¢t. It is to be observed that 
f(v) must be of such a nature as to vanish for all values of v which 
exceed a very small amount. 
Even though f(v) were a function of the angle vy makes with 
the normal to the surface, it is evident that it might be expanded 
: Que : ‘ 
in powers of =, since v is very small compared with a, and hence 
the final form of N would be unaltered. 
t 
Now @-b=?. Fe = Las Tah: since @ is very large indeed 
compared with ¢, so that calling 
Nee frat 
and Nob = 2 frtat 
both these integrals being taken between ¢=0 and ¢=that small 
value for which », must vanish, we get 
N— NG + >) 
Ch 
Similarly, for the particles entering from a small distance out- 
peas, 
Now, N, and N,’ are obviously the numbers leaving and enter- 
ing the surface when it isplane. Hence, we get that the number 
of molecules leaving is greater, and of those entering less, than in 
the case of a plane Sis 
This is obvious geometrically, because to a path of given length 
in the emitting stratum there corresponds a greater angular 
aperture for emission in the case of the spherical cue EY: in 
that of the plane. 
If we now suppose that the number entering the plane surface 
side, 
